Methodology & Research Programme

Interrelation between Human Laws and Laws of Nature

λX = EX/MX · Avv. Dr. Gian Marco Solas · 2026

The scanner is the first empirical instrument of the Theory of Interrelation — a legal-physics framework proposing that human law is a measurable physical variable, present in the equations of thermodynamics, quantum mechanics, and relativity (special and general) but never previously identified as such. This page documents the variables and formulas currently instrumented in the scanner, and the open research programme awaiting validation by physicists, mathematicians, and neuroscientists.

Based on JLMI 1/25 (Scopus)Empirical dataset in constructionCollaboration open

© Intellectual property

The legal-physics framework is the original work of Avv. Dr. Gian Marco Solas (PhD Maastricht/Cagliari · LLM College of Europe). Published in the Journal of Law, Market & InnovationJLMI 1/25, DOI 10.13135/2785-7867/12266. Full mathematical framework in "Law is Love" — SSRN 5694423 and De Lege et Amore (ISBN 9791221030631), to be published following empirical validation. © 2025–2026 Avv. Dr. Gian Marco Solas. All rights reserved.

Theoretical foundation

The framework builds on three published contributions. The Shavell standard model (Cambridge University Press, 2019) — the established rational claim condition c < λ(R) — was extended by the author for third-party funding valuation and empirically validated in the European truck cartel collective redress initiative (+/- €300M, to be ascertained judicially or in settlement).

This was generalised to entire legal systems in JLMI 2025: λX = EX/MX measures the ratio of expressed potential to total legal mass in any system, using UN SDGs as universal benchmark. Empirically tested in Masainas, Sardinia (270 comuni, €21.65B net unexpressed value identified). The algorithm at this stage tests in particular equation [4] of the paper, λ=C².

📐 Unexpressed value — preliminary estimates · λX = EX/MX
🇮🇹
#1
€384B
Italy
🇫🇷
#2
€302B
France
🇪🇸
#3
€273B
Spain
🇩🇪
#4
€263B
Germany
🇵🇱
#5
€248B
Poland
🇪🇺
Total
€5.2T
EU-27
Approximate estimates — pending full empirical confirmation. Derived from the λX = EX/MX methodology applied to national legal systems using Masainas as the validated baseline. Calculation is being extended worldwide at 1love.works.
Classical vs quantum — what is instrumented
Currently instrumented in scanner (classical physics — innovated and applied to legal systems)
· Newton (MAλ=FXλ) — legal force and acceleration
· Carnot (PC→λC→λS) — motive power, work cycles
· Joule (PC=λCF) — fee as legal energy / friction
· Einstein → λ = C² (JLMI 2025) · Newton → λW = MG (Law is Love) — law as light, legal weight
· Boltzmann (λS=k·logW) — entropy of legal microstates
Theoretically developed — pending instrumentation
· Entanglement — individuals cannot be described independently of their legal system
· Quantum jump — legal codification transitions (paradigm shifts)
· Superposition — law as particle and wave (formula [5])
· Planck threshold — minimum legal activation energy
Formulas
[1]
λX = EX/MX
Codification of Legal Systems
JLMI 2025 — ESTABLISHED
[2]
λS = k · log W(λ)
Legal Entropy — Boltzmann Renewed
Law is Love — SSRN 5694423
[3]
MAλ = FXλ
Newton's Second Law Applied to Law
Law is Love — SSRN 5694423
[3b]
PC → λC → λS
Legal Work Cycle — Inter Partes and Erga Omnes
Law is Love — SSRN 5694423
[4]
PC = λCF
Legal Friction Formula (Joule)
Law is Love — SSRN 5694423
[5]
λ = C²
Law as Light — Author's Proposition
JLMI 2025 — Published · Law is Love — extended
[6]
π = λ(R − C)
Sustainable Investment Formula
Law is Love — SSRN 5694423
[7]
λW = MG(λ) ≈ Λ
Legal Weight and Gravitational Curvature — Newton/Einstein → λW = MG
Law is Love — SSRN 5694423
[8]
S = k · log W(λ)
Boltzmann Entropy Extended to Legal Systems
Law is Love — SSRN 5694423
Open research programme

Each question is labelled: ESTABLISHED (empirically validated), STRONG HYPOTHESIS (grounded in published science), HYPOTHESIS (mathematically formulated, awaiting physics validation), or OPEN QUESTION (research direction). The legal and economic foundations are the author's competence. The physics, mathematics and neuroscience validation is the work of the scientific team.

1. Mathematical Genealogy of λ
2. Physics Hypotheses
3. Information Theory and Thermodynamics
4. Neuroscience and the Attention Economy
5. Legal and Economic Research Questions
Summary table
ESTABLISHED
Shavell c < λ(R) extension for TPF
Legal economists
ESTABLISHED
λX = EX/MX for legal systems
Legal economists, data scientists
ESTABLISHED
Human inertia vs rational actor
Behavioural economists, legal theorists
STRONG HYPOTHESIS
BCM + attention economy
Computational neuroscientists
HYPOTHESIS
De Broglie unification
Physicists, mathematicians
HYPOTHESIS
Λ = π/φ cosmological constant
Mathematicians, physicists
HYPOTHESIS
Three-way λ unification
Theoretical physicists
HYPOTHESIS
Gödel rotating universe + legal cycles
Mathematicians, physicists
HYPOTHESIS
Dirac light cone + legal causality
Physicists, legal theorists
HYPOTHESIS
Planckian threshold in law
Physicists, legal theorists
HYPOTHESIS
Einstein's elevator + Fibonacci pair
Physicists, mathematicians
HYPOTHESIS
EM/gravity/quantum unification
Theoretical physicists
HYPOTHESIS
Shannon entropy + λX equivalence
Information theorists, mathematicians
HYPOTHESIS
Maxwell's Demon → Angel
Physicists, information theorists
HYPOTHESIS
Eddington arrow + legal progress
Physicists, legal theorists
HYPOTHESIS
Brownian motion + lawyer agents
Physicists, legal economists
STRONG HYPOTHESIS
Legal weight + IPO structure
Legal economists, civil lawyers
OPEN QUESTION
DNA = natural rights foundation
Legal philosophers, biologists
OPEN QUESTION
Proprietary entity code + fractal cross-pollination©
Legal philosophers, computer scientists, governance theorists
OPEN QUESTION
Embodied skill preservation
Neuroscientists, AI researchers
Personal note — the simulation hypothesis
PERSONAL PHILOSOPHICAL OBSERVATION — NOT A SCIENTIFIC CLAIM

The convergence of Λ = π/φ (if confirmed), the Fibonacci pair as the universal generative unit, the Gödelian rotation of historical cycles, and the personal coincidences documented in the author's research — together suggest that the universe may be designed with mathematical precision at every scale. This is consistent with the simulation hypothesis (Bostrom, Tegmark) and with the theological proposition of De Lege et Amore: that Justice is the mathematical expression of Universal Love, and that Love is the constitution — discoverable, not invented. The author does not present this as a scientific claim. It is the personal motivation for the research programme. Whether it is true is not for the author to determine. It is included here because intellectual honesty requires disclosing the motivations that drive a research programme — not just its conclusions.

Note on reproducibility

The scanner is designed primarily as a scientific instrument — the same document should produce consistent scores. Current beta version uses LLM-based scoring which introduces variance. The two-call architecture (extraction + analysis) and score calibration are in active development. Every scan contributes to the empirical dataset. Methodology updates will be versioned and documented here. This is work in progress. Results may contain errors — of measurement, interpretation, or legal application. Reports, corrections and scientific collaborations are welcome.

Scientific collaboration

The author's competence is in the legal and economic foundations: litigation funding, competition law, GDPR, EU regulatory frameworks, and the λX codification methodology. The physics, mathematics and neuroscience validation is explicitly the work of the scientific team. The author is not a physicist. He is a lawyer who studied physics and identified a missing variable. Finding out whether that variable belongs in the equations is the work of those who built the equations.

✉ gmsolas@sustainab-law.eu